4 The input of a function is the independent variableThe input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

5 Directions: Identify the independent and dependent variablesin the situation.

6 Example 1A painter must measure a room before deciding how much paint to buy.The amount of paint depends on the measurement of a room.Dependent: amount of paintIndependent: measurement of the room

7 Example 2The height of a candle decrease d centimeters for every hour it burns.The height of a candle depends on the number of hours it burns.Dependent: height of candleIndependent: time

8 Example 3A veterinarian must weight an animal before determining the amount of medication.The amount of medication depends on the weight of an animal.Dependent: amount of medicationIndependent: weight of animal

9 Helpful HintThere are several different ways to describe the variables of a function.IndependentVariableDependentVariablex-valuesy-valuesDomainRangeInputOutputxf(x)

10 Example 4A company charges $10 per hour to rent a jackhammer.The cost to rent a jackhammer depends on the length of time it is rented.Dependent variable: costIndependent variable: time

11 Example 5Camryn buys p pounds of apples at $0.99 per pound.The cost of apples depends on the number of pounds bought.Dependent variable: costIndependent variable: pounds

12 You can think of a function as an input-output machine.x2You can think of a function as an input-output machine.6functionf(x)=5x5x1030output